CALCULUS AB
SECTION I. Part B
Time50 minutes
Number of questions 17
A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON
THIS PART OF THE EXAMINATION.
Directions: Solve each of the following problems, using the available space for scratchwork. After
AP Calculus 1st Semester Exam Main Points and Suggested Problems
equations of lines
domain and range of functions
growth rate
find equations for tangent and normal lines
Find limits algebraically
Determine end behavior of functions
Identify vertical and
PRODUCT RULE AND QUOTIENT RULE
Differentiate. Use proper notation and simplify your final answers. In some cases it might be
advantageous to simplify/rewrite first.
1. f ( x) (1 x )( x 3 )
3. h( y )
1
y 2 y 1
3
5. y x 3 (2 x 2 4)
7. y
x
3
x 1
2
2. g (t
LIMITS & CONTINUITY Review Sheet
NAME_
1. Find each limit. Include a table of values to illustrate your answer. Include two tables if you need to consider
a two sided limit.
A. lim(1 + x )1 x =
B. lim
y2 + 2
=
5y 6
D. lim
+
0
x0
C. lim
y
t 1
sin(2 )
=
1
MATH 171 - Derivative Worksheet
Dierentiate these for fun, or practice, whichever you need. The given answers are not simplied.
1. f (x) = 4x5 5x4
2. f (x) = ex sin x
3. f (x) = (x4 + 3x)1
4. f (x) = 3x2 (x3 + 1)7
5. f (x) = cos4 x 2x2
6. f (x) =
x2 1
x
7
Implicit Differentiation
a) With respect to x
1. x 2 y + xy 2 = 6
2. x 3 ! xy + y 3 = 1
3. 2xy + y 2 = x + y
4. x 2 (x ! y)2 = x 2 ! y 2
5. y 2 =
x !1
x +1
6. x 2 =
x!y
x+y
7. x = tan y
8. x + sin y = xy
b) Find the slope at the given point
1. y 2 + x 2 =